I recently went through the great J pickup conundrum for a build. My aim was a pretty classic, passive Jazz bass tone. If you go for something similar then I think you'll struggle to sound out of place in pretty much any situation IMO.
I ended up with a set of Nordstrand SVs and am very impressed with them. They'll give you a nice, balanced J bass tone with textured mids, tight low end and a crisp but not harsh top. If you want to drop a pre-amp in later I've mated mine with a Nordstrand circuit which is also very good.
I have a set of Nordstrand SEs in also. They too are impressive. A bit less texture and top than the SVs but a bit more thickness.
The only other
Js I could recommend would be the DiMarzio Ultra
Js. Again very nice and gave a great new lease of life to my old Squire Jazz.
I have a set of EMGs also but personally I'm not really into them. They sound very smooth, ultra highs and ultra lows which to me isn't really what the J bass (and bass in general) is about.
Are there particular players or tracks that you like the sound of? One man's "punchy funk tone" is another man's "nasty, toppy ping-fest"
